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    NSPACE(f(n)) is a subset of TIME(2^O(f(n))) — Carmelics
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    Home/Modality & Possibility
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    NSPACE(f(n)) is a subset of TIME(2^O(f(n)))

    Modality & PossibilityTruth & Knowledge
    ?Rate how convincing each reason is below to see the overall strength.
    1 reason for
    2 reasons against

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.f(n) is both time and space constructible
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    • 2.A non-deterministic machine with space bound f(n) can be simulated deterministically in exponential time
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    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 1.The simulation argument presupposes that non-deterministic computation is reducible to deterministic processes without epistemic loss.
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    • 2.Kripke's possible-worlds semantics suggests non-deterministic branching represents genuinely distinct modal trajectories, not mere syntactic abbreviation.
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    • 3.If non-determinism tracks real modal structure, the exponential blowup in simulation reflects ontological inflation, not mere computational overhead, undermining the subset claim's scope.
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    Reason against 2 of 2
    ?
    • 1.The claim that NSPACE(f(n)) ⊆ TIME(2^O(f(n))) relies on f(n) being space-constructible, a condition that smuggles in a non-trivial computability assumption.
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    • 2.Constructibility requirements, as Blum's axioms show, are not purely formal but encode substantive constraints on what counts as a legitimate resource measure.
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    • 3.A complexity inclusion whose proof boundary depends on contested resource-theoretic assumptions cannot be taken as a necessary truth about computational possibility.
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    Related

    A complexity inclusion whose proof boundary depends on contested resource-theore...A non-deterministic machine with space bound f(n) can be simulated deterministic...Constructibility requirements, as Blum's axioms show, are not purely formal but ...If non-determinism tracks real modal structure, the exponential blowup in simula...
    +4 moreShow less
    Kripke's possible-worlds semantics suggests non-deterministic branching represen...The claim that NSPACE(f(n)) ⊆ TIME(2^O(f(n))) relies on f(n) being space-constru...The simulation argument presupposes that non-deterministic computation is reduci...f(n) is both time and space constructible

    Similar

    NTIME(f(n)) is a subset of SPACE(f(n))100%PSPACE is a subset of NPSPACE (PSPACE ⊆ NPSPACE)84%P is a subset of NP (P ⊆ NP)84%PSPACE is a subset of NPSPACE82%

    Source

    AI-extracted1/3 agreementValid
    SEP: computational-complexity
    View source passageHide passage
    2 Complexity classes and the hierarchy theorems Recall that a complexity class is a set of languages all of which can be decided within a given time or space complexity bound \(t(n)\) or \(s(n)\) with respect to a fixed model of computation. g. non-recursive ones) it is standard to restrict attention to complexity classes defined when \(t(n)\) and \(s(n)\) are time or space constructible. e. a string of \(n\) 1s) halts after exactly \(t(n)\) steps. Similarly, \(s(n)\) is said to be space constru
    Extraction notes

    Validity: Extracted via Max plan + API grounding/validity checks

    Details

    Type
    claim
    Perspectives
    3 (1 for, 2 against)
    Edits
    1 edit